Essay On Euclid Of Alexandria

This text is organized chronologically and provides interesting information about the details of the mathematicians' lives.At the time, and for many centuries, Euclid's work was simply called "geometry" because it was assumed to be the only possible method of describing space and the position of figures.

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It would be folly, in a book of this scope, to expect that every date, as well as every decimal point, is correct. A third explanation holds that the expulsion was coupled with the disclosure of a mathematical discovery of devastating significance for Pythagorean philo- sophy — the existence of incommensurable magnitudes.

I have striven to avoid such an attitude, and the purpose of the book is to present the history of mathematics with fidelity, not only to mathematical structure and exacti- tude, but also to historical perspective and detail. A second tradition attributes the expulsion to disclosures concerning the geometry of the pentagon or the dodecahedron — perhaps a construction of one of the figures.

Euclid of Alexandria lived in 365-300 BC (approximately).

Mathematicians usually refer to him simply as "Euclid," but he's sometimes called Euclid of Alexandria to avoid confusion with the Green Socratic philosopher Euclid of Megara.

In a work of modest scope the author must exercise judgment in the selection of the materials to be included, reluctantly restraining the temptation to cite the work of every productive mathematician ; it will be an exceptional reader who will not note here what he regards as unconscionable omissions. They do not suffice, for example, to compare the diagonal of a square or a cube or a pentagon with its side.

Such an enterprise would call for the concerted effort of a team, similar to that which produced the fourth volume of Cantor's Vorlesungen uber Geschichte der Mathematik in 1908 and brought the story down to 1799. This was the discovery that within geometry itself the whole numbers and their ratios are inadequate to account for even simple fundamental properties.

The present work differs from the most successful presently available textbook in a stricter adherence to the chronological arrangement and a stronger emphasis on historical elements. One account has it that the Pythagor- eans erected a tombstone to him, as though he were dead; another story reports that his apostasy was punished by death at sea in a shipwreck.

Besides providing important additional sources for those who have a reading knowledge of a foreign language, the inclusion of references in other lan- guages may help to break down the linguistic provincialism which, ostrich- like, takes refuge in the mistaken impression that everything worthwhile appeared in, or has been translated into, the English language. 79 THE HEROIC AGE Hippasus of Metapontum (or Croton), roughly contemporaneous with Philolaus, is reported to have been originally a Pythagorean but to have been expelled from the brotherhood.

It cannot be too strongly emphasized that this single volume in no way purports to present the history of mathematics in its entirety. The dialogues of Plato show, however, that the Greek mathematical community had been stunned by a disclosure that virtually demolished the basis for the Pythagorean faith in whole numbers.

It is hoped, however, that such inadvertencies as may survive beyond the stage of page proof will not do violence to the sense of history, broadly understood, or to a sound view of mathematical concepts. It had been a fundamental tenet of Pythagoreanism that the essence of all things, in geometry as well as in the practical and theoretical affairs of man, are explainable in terms of arithmos, or intrinsic properties of whole numbers or their ratios.


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